Package: onion 1.5-4
onion: Octonions and Quaternions
Quaternions and Octonions are four- and eight- dimensional extensions of the complex numbers. They are normed division algebras over the real numbers and find applications in spatial rotations (quaternions), and string theory and relativity (octonions). The quaternions are noncommutative and the octonions nonassociative. See the package vignette for more details.
Authors:
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onion.pdf |onion.html✨
onion/json (API)
| # Install 'onion' in R: |
| install.packages('onion', repos = c('https://robinhankin.r-universe.dev', 'https://cloud.r-project.org')) |
Bug tracker:https://github.com/robinhankin/onion/issues
Last updated 22 days agofrom:6098f09abb. Checks:OK: 9. Indexed: yes.
| Target | Result | Date |
|---|---|---|
| Doc / Vignettes | OK | Aug 27 2024 |
| R-4.5-win-x86_64 | OK | Aug 27 2024 |
| R-4.5-linux-x86_64 | OK | Aug 27 2024 |
| R-4.4-win-x86_64 | OK | Aug 27 2024 |
| R-4.4-mac-x86_64 | OK | Aug 27 2024 |
| R-4.4-mac-aarch64 | OK | Aug 27 2024 |
| R-4.3-win-x86_64 | OK | Aug 27 2024 |
| R-4.3-mac-x86_64 | OK | Aug 27 2024 |
| R-4.3-mac-aarch64 | OK | Aug 27 2024 |
Exports:%.%%<.>%%<*>%%>.<%%>*<%adas.matrixas.octonionas.onionas.onionmatas.orthogonalas.quaternionassociatorbiggestbind_onionbind_onion_onionbind_onion_onionmatbind_onionmat_onionbind_onionmat_onionmatc_onionpaircolnamescolnames<-commutatorcomp_namescondensecproddiagdiag<-dotproddropgetdgetMH0H1Hallharmonize_onharmonize_ooherm_onion_matHiHimHjHkhtii<-ilil<-Im<-is.octonionis.onionis.onionmatis.quaternionjj<-jljl<-kk<-klkl<-ll<-matrixmatrix_arith_onionmatrix_arith_onionmatmatrix_plus_onionmatrix_prod_onionmatrix2quaternionncolnewonionmatNormnrownumeric_arith_onionnumeric_matrixprod_onionmatO0O1Oalloctonionoctonion_prod_octonionoctonion_to_quaternionOiOilOimOjOjlOkOklOlom_cprodom_htom_tcprodonion_absonion_acosonion_acoshonion_allsumonion_arith_matrixonion_arith_numericonion_arith_oniononion_asinonion_asinhonion_atanonion_atanhonion_compareonion_complexonion_conjugateonion_cosonion_coshonion_cumprodonion_cumsumonion_e_evenonion_e_oddonion_exponion_g_evenonion_g_oddonion_imagonion_inverseonion_logonion_logiconion_matrixprod_onionmatonion_modonion_negativeonion_plus_numericonion_plus_oniononion_power_matrixonion_power_numericonion_power_singleintegeronion_prod_numericonion_prod_oniononion_reonion_showonion_signonion_sinonion_sinhonion_sqrtonion_tanonion_tanhonion_to_stringonion_to_string_lowlevelonionmatonionmat_allsumonionmat_arith_matrixonionmat_arith_onionmatonionmat_arith_singleonionmat_compare_onionmatonionmat_compare_singleonionmat_complexonionmat_conjugateonionmat_equal_onionmatonionmat_equal_singleonionmat_imagonionmat_inverseonionmat_matrixprod_numericonionmat_matrixprod_oniononionmat_matrixprod_onionmatonionmat_modonionmat_negativeonionmat_plus_matrixonionmat_plus_onionmatonionmat_plus_singleonionmat_power_matrixonionmat_power_onionmatonionmat_power_singleonionmat_prod_matrixonionmat_prod_onionmatonionmat_prod_singleonionmat_reonionmat_showp3dplotquaternionquaternion_allprodquaternion_prod_quaternionquaternion_to_octonionRe<-roctromatrotaterownamesrownames<-rquatrsoctrsomatrsquatseqseq_onionsingle_arith_onionmatsingle_compare_onionmatsingle_power_onionmatsingle_prod_onionmatstrstr_onionttcprodthreeformzapsmall
Dependencies:digestdisordRfreealggmplatticemathjaxrMatrixpartitionspolynomquadformrbibutilsRcppRdpacksets
Matrices with quaternion or octonion entries: class onionmat in the onion package
Rendered fromonionmat.Rmdusingknitr::rmarkdownon Aug 27 2024.Last update: 2023-10-03
Started: 2020-12-10
The onion package
Rendered fromonionpaper.Rnwusingutils::Sweaveon Aug 27 2024.Last update: 2024-06-03
Started: 2018-05-17
Readme and manuals
Help Manual
| Help page | Topics |
|---|---|
| Octonions and Quaternions | onion-package |
| The adjoint map | ad adjoint |
| Methods for Function Arith in package Onion | Arith Arith,ANY,onion-method Arith,onion,ANY-method Arith,onion,missing-method Arith,onion,numeric-method Arith,onion,onion-method Arith-methods harmonize_on harmonize_oo numeric_arith_onion octonion_prod_octonion onion_arith_numeric onion_arith_onion onion_inverse onion_negative onion_plus_numeric onion_plus_onion onion_power_numeric onion_power_singleinteger onion_prod_numeric onion_prod_onion quaternion_prod_quaternion |
| Returns the biggest type of a set of onions | biggest |
| Binding of onionmats | bind bind_onion bind_onionmat_onion bind_onionmat_onionmat bind_onion_matrix bind_onion_onion bind_onion_onionmat cbind cbind2,matrix,onion-method cbind2,matrix,onionmat-method cbind2,numeric,onion-method cbind2,numeric,onionmat-method cbind2,onion,matrix-method cbind2,onion,numeric-method cbind2,onion,onion-method cbind2,onion,onionmat-method cbind2,onionmat,matrix-method cbind2,onionmat,numeric-method cbind2,onionmat,onion-method cbind2,onionmat,onionmat-method rbind rbind2,matrix,onion-method rbind2,matrix,onionmat-method rbind2,numeric,onion-method rbind2,numeric,onionmat-method rbind2,onion,matrix-method rbind2,onion,numeric-method rbind2,onion,onion-method rbind2,onion,onionmat-method rbind2,onionmat,matrix-method rbind2,onionmat,numeric-method rbind2,onionmat,onion-method rbind2,onionmat,onionmat-method |
| The Stanford Bunny | bunny |
| Concatenation | c c,onion-method c.onion concatenate.onion c_onionpair |
| Methods for compare S4 group | Compare,ANY,onionmat-method Compare,numeric,onion-method Compare,onion,numeric-method Compare,onion,onion-method Compare,onionmat,ANY-method Compare,onionmat,onionmat-method Compare-methods onionmat_compare_onionmat onionmat_compare_single onionmat_equal_onionmat onionmat_equal_single onion_compare single_compare_onionmat |
| Complex functionality for onions | Conj Conj,onion-method Conj,onionmat-method Im Im,onion-method Im,onionmat-method Im<- Im<-,onion-method Im<-,onionmat-method Mod Mod,onion-method Mod,onionmat-method Norm Norm,onion-method Norm,onionmat-method Norm.onion onion_abs onion_complex onion_conjugate onion_imag onion_mod onion_re Re Re,onion-method Re,onionmat-method Re<- Re<-,onion-method Re<-,onionmat-method sign,onion-method |
| Condense an onionic vector into a short form | condense condense.onion |
| Cumulative sums and products of onions | cumsum onion_cumprod onion_cumsum |
| Class "dot" | . dot dot-class dot_error extract jacobi [,dot,ANY,ANY,ANY-method [,dot,ANY,ANY-method [,dot,ANY,missing,ANY-method [,dot,ANY,missing-method [,dot,function,function,ANY-method [,dot,function,function-method [,dot,matrix,matrix,ANY-method [,dot,matrix,matrix-method [,dot,missing,ANY,ANY-method [,dot,missing,ANY-method [,dot,missing,missing,ANY-method [,dot,missing,missing-method [,dot-method [.dot |
| Drop zero imaginary parts of an onionic vector | drop drop,onion-method drop,onionmat-method drop.onion |
| Extract or Replace Parts of onions or glubs | i i,onion-method i,onionmat-method i.octonion i.quaternion i<- i<-,onion-method i<-,onionmat-method i<-.octonion i<-.quaternion il il,octonion-method il,onionmat-method il.octonion il<- il<-,octonion-method il<-,onionmat-method il<-.octonion Im<-.quaternion j j,onion-method j,onionmat-method j.octonion j.quaternion j<- j<-,onion-method j<-,onionmat-method j<-.octonion j<-.quaternion jl jl,octonion-method jl,onionmat-method jl.octonion jl<- jl<-,octonion-method jl<-,onionmat-method jl<-.octonion k k,onion-method k,onionmat-method k.octonion k.quaternion k<- k<-,onion-method k<-,onionmat-method k<-.octonion k<-.quaternion kl kl,octonion-method kl,onionmat-method kl.octonion kl<- kl<-,octonion-method kl<-,onionmat-method kl<-.octonion l l,octonion-method l,onion-method l,onionmat-method l.octonion l<- l<-,octonion-method l<-,onionmat-method l<-.octonion Re<-.quaternion [ [,onion,ANY,ANY-method [,onion,index,ANY,ANY-method [,onion,index,ANY-method [,onion,index,missing,ANY-method [,onion,index,missing-method [,onion-method [,onionmat,ANY,ANY,ANY-method [,onionmat,ANY,ANY-method [,onionmat,index,index,ANY-method [,onionmat,index,index-method [,onionmat,index,missing,ANY-method [,onionmat,index,missing,missing-method [,onionmat,index,missing-method [,onionmat,matrix,missing,ANY-method [,onionmat,matrix,missing-method [,onionmat,missing,index,ANY-method [,onionmat,missing,index-method [,onionmat,missing,missing,ANY-method [,onionmat,missing,missing-method [.onion [<- [<-,onion,ANY,ANY-method [<-,onion,index,ANY,ANY-method [<-,onion,index,missing,ANY-method [<-,onion,index,missing,numeric-method [<-,onion,index,missing,onion-method [<-,onion,missing,missing,numeric-method [<-,onion,missing,missing,onion-method [<-,onion-method [<-,onionmat,ANY,missing,numeric-method [<-,onionmat,ANY,missing,onion-method [<-,onionmat,index,index,numeric-method [<-,onionmat,index,index,onion-method [<-,onionmat,index,missing,numeric-method [<-,onionmat,index,missing,onion-method [<-,onionmat,missing,index,numeric-method [<-,onionmat,missing,index,onion-method [<-.onion |
| Length of an octonionic vector | length length,onion-method length.onion length<- length<-,onion-method length<-.onion |
| Logical operations on onions | Logic,ANY,onion-method Logic,onion,ANY-method Logic,onion,missing-method Logic,onion-method logic.onion onion_logic |
| Various logarithmic and circular functions for onions | abs,onion-method acos acos,onion-method acosh acosh,onion-method asin asin,onion-method asinh asinh,onion-method atan atan,onion-method atanh atanh,onion-method cos cos,onion-method cosh cosh,onion-method exp exp,onion-method log log,onion-method onion_acos onion_acosh onion_asin onion_asinh onion_atan onion_atanh onion_cos onion_cosh onion_exp onion_log onion_sign onion_sin onion_sinh onion_sqrt onion_tan onion_tanh sin sin,onion-method sinh sinh,onion-method sqrt tan tan,onion-method tanh tanh,onion-method |
| Names of an onionic vector | colnames colnames,onion-method colnames,onionmat-method colnames<-,onionmat-method dim dim,onionmat-method dim<- dim<-,onionmat-method dimnames,onionmat-method dimnames<-,onionmat,ANY-method dimnames<-,onionmat-method names,onion-method names,onionmat-method names.onion names.onion<- names<- names<-,onion-method names<-,onionmat-method names<-.onion ncol,onionmat-method nrow,onionmat-method rownames rownames,onionmat-method rownames<-,onionmat-method |
| Unit onions | H0 H1 Hall Hi Him Hj Hk O0 O1 Oall Oi Oil Oim Oj Ojl Ok Okl Ol |
| Basic onion functions | as.matrix as.matrix,onion-method as.numeric,onion-method as.octonion as.onion as.quaternion is.octonion is.onion is.quaternion Octonion octonion octonion_to_quaternion onion Quaternion quaternion quaternion_to_octonion type |
| Class "onion" | index-class octonion-class onion-class onionmat-class quaternion-class |
| Onionic matrices | %*% %*%,numeric,onion-method %*%,numeric,onionmat-method %*%,onion,onionmat-method %*%,onionmat,numeric-method %*%,onionmat,onion-method %*%,onionmat,onionmat-method +,onion,missing-method +,onionmat,missing-method -,onion,missing-method -,onionmat,missing-method as.octonionmat as.onionmat as.quaternionmat colnames<- cprod cprod,ANY,ANY-method cprod,ANY,missing-method cprod,ANY,onionmat-method cprod,onion,missing-method cprod,onion,onion-method cprod,onion,onionmat-method cprod,onionmat,ANY-method cprod,onionmat,missing-method cprod,onionmat,onion-method cprod,onionmat,onionmat-method diag diag,onion-method diag,onionmat-method diag.onion diag.onionmat diag<-,onionmat-method diag<-.onionmat getd getM herm_onion_mat ht ht,onion-method ht,onionmat-method is.onionmat matrix,onion-method matrix_arith_onion matrix_arith_onionmat matrix_plus_onion matrix_plus_onionmat matrix_prod_onion ncol ncol,ANY-method ncol-methods ncol.onionmat newonionmat nrow nrow,ANY-method nrow-methods nrow.onionmat numeric_arith_onionmat numeric_matrixprod_onionmat om_cprod om_ht om_prod om_tcprod onionmat onionmatprod onionmat_arith_matrix onionmat_arith_onion onionmat_arith_onionmat onionmat_arith_single onionmat_complex onionmat_conjugate onionmat_imag onionmat_inv onionmat_inverse onionmat_matrixprod_numeric onionmat_matrixprod_onion onionmat_matrixprod_onionmat onionmat_mod onionmat_neg onionmat_negative onionmat_plus_matrix onionmat_plus_onionmat onionmat_plus_single onionmat_power_matrix onionmat_power_onionmat onionmat_power_single onionmat_prod_matrix onionmat_prod_onionmat onionmat_prod_single onionmat_re onionmat_unary onion_arith_matrix onion_arith_onionmat onion_arith_single onion_matrixprod_onionmat onion_power_matrix Ops.onionmat rownames,ANY-method rownames-methods rownames.onionmat rownames<- rownames<-,ANY-method rownames<--methods rownames<-.onionmat single_arith_onionmat single_power_onionmat single_prod_onionmat t,onion-method t,onionmat-method t.onion t.onionmat tcprod tcprod,ANY,ANY-method tcprod,ANY,missing-method tcprod,ANY,onionmat-method tcprod,onion,missing-method tcprod,onion,onion-method tcprod,onion,onionmat-method tcprod,onionmat,ANY-method tcprod,onionmat,missing-method tcprod,onionmat,onion-method tcprod,onionmat,onionmat-method [.onionmat [<-.onionmat |
| Orthogonal matrix equivalents | as.orthogonal is_orthogonal matrix2quaternion orthogonal |
| Three dimensional plotting | p3d |
| Plot onions | plot plot,onion-method plot.onion |
| Various products of two onions | %.% %<*>% %<*>%.onion %<.>% %<.>%.onion %>*<% %>*<%.onion %>.<% %>.<%.onion dotprod e_even.onion e_odd.onion g_even.onion g_odd.onion onion_e_even onion_e_odd onion_g_even onion_g_odd prods |
| Replicate elements of onionic vectors | rep rep,onion-method rep.onion |
| Random onionic vectors | roct romat ronionmat rquat rsoct rsomat rsquat |
| Rotates 3D vectors using quaternions | rotate |
| Rounding of onions | round round,onion-method round,onionmat-method |
| seq method for onions | seq seq,onion-method seq.onion seq_onion SLERP slerp |
| Print method for onions | comp_names onionmat_show onion_show onion_to_string onion_to_string_lowlevel print print,onion-method print.octonion print.onion print.onionmat print.quaternion show show,onion-method |
| Various summary statistics for onions | max min onionmat_allsum onion_allsum prod prod,octonion-method prod,quaternion-method quaternion_allprod range str,onion-method str_onion sum sum,octonion-method sum,onion-method sum,onionmat-method sum,quaternion-method Summary,onion-method |
| Various non-field diagnostics | associator commutator threeform |
| Concatenation | zap zapsmall zapsmall,onion-method zapsmall,onionmat-method |
